New Variational Principles for Two Kinds of Nonlinear Partial Differential Equation in Shallow Water

Document Type : Research Paper


1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China

2 College of Computer, National University of Defense Technology, Changsha 410073, China


Variational principles are very important for a lot of nonlinear problems to be analyzed theoretically or solved numerically. By the popular semi-inverse method and designing trial-Lagrange functionals skillfully, new variational principles are constructed successfully for the Kuramoto-Sivashinsky equation and the Coupled KdV equations, respectively, which can model a lot of nonlinear waves in shallow water. The established variational principles are also proved correct. The procedure reveals that the used technologies are very powerful and applicable, and can be extended to other nonlinear physical and mathematical models.


Main Subjects

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